{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T18:08:43Z","timestamp":1788804523080,"version":"build-2803163510"},"reference-count":34,"publisher":"L and H Scientific Publishing, LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JEAM"],"published-print":{"date-parts":[[2027,3,1]]},"abstract":"<jats:p>This paper investigates the dynamics of a chaotic system using the fractal-fractional derivative with a power-law kernel. We extend a classical financial model described by nonlinear coupled ordinary differential equations into the fractal-fractional domain to better capture its complex behaviors. This study includes comprehensive theoretical analyses, specifically the determination of equilibrium points, existence and uniqueness of solutions, and verification of Ulam stability. Our analysis demonstrates that the fractal-fractional approach reveals patterns and behaviors not evident in the classical-order model. The numerical simulations confirm the theoretical findings and illustrate how varying the fractal and fractional orders affects the system's dynamics. This research provides a mathematically rigorous framework for analyzing financial market volatility, offering a foundation for more accurate financial forecasting and risk assessment.<\/jats:p>","DOI":"10.5890\/jeam.2027.03.010","type":"journal-article","created":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T17:41:02Z","timestamp":1788802862000},"page":"161-182","source":"Crossref","is-referenced-by-count":0,"title":["Chaotic Dynamics in Financial Systems Using Fractal-Fractional Derivatives with a Power-Law Kernel"],"prefix":"10.5890","volume":"15","author":[{"given":"R.","family":"Gandhimathi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Gowrisankar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"7015","published-online":{"date-parts":[[2026,9,7]]},"reference":[{"key":"ref1","unstructured":"[1] Podlubny, I. 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